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Reaction–diffusion equation based image restoration

Author

Listed:
  • Zhao, Xueqing
  • Huang, Keke
  • Wang, Xiaoming
  • Shi, Meihong
  • Zhu, Xinjuan
  • Gao, Quanli
  • Yu, Zhaofei

Abstract

We present a novel restoration algorithm based on the reaction–diffusion equation theory, denominated RDER, for restoring images which are corrupted by various blur PSFs and different types of noise (including different levels of impulse noise, Gaussian noise and mixed noise). The focus of this work is to propose an image restoration method based on the reaction diffusion equation and to further extend the traditional diffusion equation. Firstly, the RDER model is constructed by using the restoration ability of the diffusion equation, and the image detail preservation ability of the reaction equation; secondly, based on the difference scheme theory, a discrete RDER model is proposed for image restoration and a RDER algorithm for restoring the image is designed; thirdly, we mathematically analyze the RDER model from the existence, stability and uniqueness of solutions of the RDER model; finally, the proposed RDER algorithm is compared with the current famous state-of-the-art restoration algorithms in image restoring and image details preserving. Theoretical analysis and extensive experimental results show that the RDER is an effective image restoration algorithm for image denoising, image deblurring and image details preserving; in particular, the RDER provides a better performance in terms of the impulse noise and mixed noise.

Suggested Citation

  • Zhao, Xueqing & Huang, Keke & Wang, Xiaoming & Shi, Meihong & Zhu, Xinjuan & Gao, Quanli & Yu, Zhaofei, 2018. "Reaction–diffusion equation based image restoration," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 588-606.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:588-606
    DOI: 10.1016/j.amc.2018.06.054
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    References listed on IDEAS

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    1. Gazzola, Silvia & Karapiperi, Anna, 2016. "Image reconstruction and restoration using the simplified topological ε-algorithm," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 539-555.
    2. Shama, Mu-Ga & Huang, Ting-Zhu & Liu, Jun & Wang, Si, 2016. "A convex total generalized variation regularized model for multiplicative noise and blur removal," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 109-121.
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    Cited by:

    1. Upadhyay, Prateep & Upadhyay, S.K. & Shukla, K.K., 2021. "Magnetic resonance images denoising using a wavelet solution to laplace equation associated with a new variational model," Applied Mathematics and Computation, Elsevier, vol. 400(C).

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